Thesis Presentation: Cellular Automata for Control and Interactions of Large Formations of Robots

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Thesis PresentationCellular Automata
forControl and Interactions ofLarge Formations
of Robots

• Ross Mead
• Committee
• Dr. Jerry B. Weinberg
• Dr. Stephen Blythe
• Dr. Xudong Yu

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Outline

• Introduction and Significance
• Comparison of Cellular Automata Approaches
• 1-Dimensional Robot-Space Cellular Automata
• Algorithm
• Implementation
• 2-Dimensional Robot-Space Cellular Automata
• Algorithm Extension
• Implementation
• Conclusions
• Future Work
• QA

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Motivation

• Space Solar Power (SSP)
• How can a massive collection of robots moving
  with no group organization coordinate to form a
  global structure?

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Problem
swarm
formation
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Approach

• Utilize reactive robot control strategies
• closely couple sensor input to actions
• Treat the formation as a cellular automaton
• lattice of computational units (cells)
• each cell is in one of a given set of states
• governed by a set of rules
• complex emergent behavior from simplicity

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World-Space Cellular Automata

• Environment is represented topologically as a 2-
  or 3-dimensional grid of cells

1. robot between grid cells
2. boundary surrounds the automaton
3. automaton wraps along boundaries
4. two robots collide trying to occupy same grid cell

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Robot-Space Cellular Automata

• Each robot is represented as a cell ci in a
  1-dimensional automaton

• ci H, s, F, S

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Robot-Space Cellular Automata

• Each robot is represented as a cell ci in a
  1-dimensional automaton

• ci H, s, F, S
• neighborhood
• Hi ci-1, ci, ci1
• ci-1 ? left neighbor
• ci1 ? right neighbor
• cj ? some neighbor j

• C ? automaton
• C H1 U H2 U U Hn
• c1, c2, , cn

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Robot-Space Cellular Automata

• Each robot is represented as a cell ci in a
  1-dimensional automaton

• ci H, s, F, S
• state
• si p, rdes, ract, G, T , t
• ( ... described later ... )

• C ? automaton
• C H1 U H2 U U Hn
• c1, c2, , cn

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Robot-Space Cellular Automata

• Each robot is represented as a cell ci in a
  1-dimensional automaton

• ci H, s, F, S
• state transition
• si p, rdes, ract, G, T , t
• ( ... described later ... )
• sit S(si-1t-1, sit-1, si1t-1)
• t ? time step (counter)

• C ? automaton
• C H1 U H2 U U Hn
• c1, c2, , cn

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Robot-Space Cellular Automata

• Each robot is represented as a cell ci in a
  1-dimensional automaton

• ci H, s, F, S
• formation
• F f(x), R, F, pseed
• f(x) ? description
• R ? robot separation
• F ? relative heading
• pseed ? start position

• C ? automaton
• C H1 U H2 U U Hn
• c1, c2, , cn

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Algorithm Formation Definition

• F is sent to some robot, designating it as the
  seed cell cseed...
• cseed is not a leader, but rather an initiator of
  the coordination process
• For purposes of calculating desired
  relationships, each cell ci considers itself to
  be at some formation-relative position pi
• pi xi f(xi) T
• In the case of cseed, this position pseed is
  given

f(x) a x2
cseed
pseed
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Algorithm Desired Relationships

• The desired relationship ri?j,des from ci to some
  neighbor cj is determined by calculating a vector
  v from pi to the intersection f(vx) and a circle
  centered at pi with radius R
• R2 (vx pi,x)2 (f(vx) pi,y)2 ri?j,des
  vx f(vx) T
• The relationship is rotated by F to account for
  robot heading...

f(x) a x2
R
v
v
desired relationship with left neighbor ci-1
desired relationship with right neighbor ci1
ri?i-1,des
ri?i1,des
pseed
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Algorithm Desired Relationships

• F and ri?j,des are communicated locally within
  the neighborhood.
• Each neighbor cj repeats the process, but
  considers itself to be at different
  formation-relative position pj
• determined by the desired relationship from the
  sending neighbor ci
• pj pi ri?j,des

f(x) a x2
Note rj?i,des ri?j,des
pi-1
pi1
pseed
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Algorithm Desired Relationships

• Propagate changes in neighborhoods in succession.
• Calculated relationships generate a connected
  graph that yields the shape of the formation.

f(x) a x2
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Algorithm Actual Relationships

• Using sensor readings, robots calculate an actual
  relationship ri?j,act with each neighbor cj.
• State of Hi governs robot movement
• rotational error Ti and translational error Gi
• relationships based on individual coordinate
  systems

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Algorithm Formation Manipulation
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Algorithm Formation Manipulation
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Algorithm Formation Manipulation
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Algorithm Formation Manipulation
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Algorithm Formation Manipulation
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Algorithm Formation Manipulation
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Implementation Robot Platform

• ZigBee module
• packet communication
• share state information
• within neighborhood

• Color-coding system
• visual identification
• neighbor localization
• (actual relationships)

• Scooterbot II base
• strong, but very light
• differential steering system

• XBCv2 microcontroller
• Interactive C
• back-EMF PID motor control
• color camera

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Implementation Color-Coding System

• Visual identification
• the color of each robot is assigned based on ID
• orange for odd, green for even
• Neighbor localization (actual relationships)
• ri?j,act di?j ai?j T

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Implementation State Diagram
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Implementation Results

• ... and because embedding Windows own media
  format is a too much for PowerPoint...
• Click Here

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Extending the Formation Definition

• Consider a set f' of M mathematical functions
• f' f1(x), f2(x), ..., fM(x) F f', R, F,
  pseed
• For desired relationships, each fm(x) is
  considered individually...
• yielding its own 1-dimensional neighborhood mhi
• resulting in M neighborhoods and a 2-dimensional
  cellular automaton (M gt 1)
• Hi 1hi U 2hi U ... U Mhi Mc1-1, , 2c1-1,
  1c1-1, c1, 1c11, 2c11, , Mc11

f2(x) x v3
f3(x) x v3
f1(x) 0
R
1hi 1ci-1, ci, ci1
2hi 2ci-1, ci, ci1
3hi 3ci-1, ci, ci1
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How can this be applied to SSP?

• Reflector viewed as 2-dimensional lattice of
  robots and, thus, a 2-dimensional cellular
  automaton...

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Multi-Function Formations
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Multi-Function Formations

• Desired relationship ri?j,des vx f(vx)
  T
• What
• happened?
• Original R2 (vx pi,x)2 (f(vx) pi,y)2

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Multi-Function Formations

• Desired relationship ri?j,des vx f(vx)
  T
• What
• happened?
• Original R2 (vx pi,x)2 (f(vx) pi,y)2
• Alternative R2 vx2 f(vx)2

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Multi-Function Formations

• Desired relationship ri?j,des vx f(vx)
  T
• Similarly...
• Original R2 (vx pi,x)2 (f(vx) pi,y)2

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Multi-Function Formations

• Similarly...
• Alternative R2 vx2 f(vx)2

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Implementation Robot Platform
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Implementation Robot Faces

• Visual identification
• each robot has a unique three-color column...
• vertical locations of color bands correspond to
  ID
• green on top for even, magenta on top for odd
• 5 locations 4 locations 20 unique faces

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Implementation Robot Faces

• All around me are familiar faces...

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Implementation Results

• Click Here

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Conclusions Algorithm

• Designed and implemented a general distributed
  robot formations algorithm...
• able to conform to a wide variety of formations
• Robots represented as cells in multi-dimensional
  cellular automata...
• simple rule sets produce complex group behavior
• Distinguishes itself as leaderless algorithm...
• only communication is to instigate coordination

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Conclusions Robot Platform

• Hardware ?

• Software ?

• 19 robots developed.
• Accurate motion control.
• Reasonable execution time.
• Reliable communication.
• Robot faces were excellent!

• Extensive and reusable collection of libraries.
• Greatest implementation hurdleInteractive C...
• most time spent debugging
• workaroundsnot fixes
• serial library deadlock
• bug list is... amusing...
• imposes harsh program size
• ... stay away!

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Conclusions Formation Classification

1. Non-formation (swarm)
2. Explicit formation
3. Straight line formation

1. Function-based formation
2. Branching formation
3. Lattice formation

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Conclusions Erroneous Relationships

• Theoretically possible to calculate more than two
  relationships...
• To alleviate this, solve for two minimums
• e(v) vx pi,x

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Future Work

• Dynamic neighborhoods
• Seed election
• Formation repair
• Obstacle avoidance
• Global positioning

• 3-dimensional formations
• Disconnected formations
• Formation classification
• Analysis Click here
• Formation management

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Questions?
For more information, please visithttp//roboti.c
s.siue.edu/projects/formations/or see the
following papers

• Mead, R. Weinberg, J.B. (2008). A Distributed
  Control Algorithm for Robots in Grid Formations.
  To appear in the Proceedings of the Robot
  Competition and Exhibition of The 23rd National
  Conference on Artificial Intelligence (AAAI-08),
  Chicago, Illinois.
• Mead, R. Weinberg, J.B. (2008). 2-Dimensional
  Cellular Automata Approach for Robot Grid
  Formations. To appear in Student Abstracts and
  Poster Program of The 23rd National Conference on
  Artificial Intelligence (AAAI-08). Chicago,
  Illinois.

• Mead, R., Weinberg, J.B., Croxell, J.R. (2007).
  A Demonstration of a Robot Formation Control
  Algorithm and Platform. To appear in the
  Proceedings of the Robot Competition and
  Exhibition of The 22nd National Conference on
  Artificial Intelligence (AAAI-07), Vancouver,
  British Columbia.
• Mead, R., Weinberg, J.B., Croxell, J.R. (2007).
  An Implementation of Robot Formations using Local
  Interactions. In the Proceedings of The 22nd
  National Conference on Artificial Intelligence
  (AAAI-07), 1889-1890. Vancouver, British Columbia.